Wavelet-based regularization of the Galerkin truncated three-dimensional incompressible Euler flows.

Area of Science:

• Fluid Dynamics
• Computational Physics
• Turbulence Modeling

Background:

• Incompressible Euler equations describe inviscid fluid flow.
• Simulating turbulence requires regularization techniques to manage computational complexity.
• Wavelet analysis offers multi-scale decomposition for signal processing.

Purpose of the Study:

• To develop and evaluate a wavelet-based denoising method for regularizing simulations of the 3D Euler equations.
• To model turbulent dissipation adaptively by filtering incoherent vorticity.
• To compare wavelet-based regularization with traditional methods.

Main Methods:

• Numerical simulations of Galerkin truncated 3D Euler equations.
• Wavelet decomposition of the vorticity field at each time step.
• Separation and reconstruction of coherent and incoherent vorticity components.
• Adaptive regularization by advancing only the coherent flow.
• Comparison with Navier-Stokes, hyperdissipative, and Euler-Voigt regularizations.

Main Results:

• Wavelet denoising successfully models turbulent dissipation.
• The coherent flow exhibits intermittent nonlinear dynamics.
• An energy spectrum proportional to k^{-5/3} was observed, characteristic of 3D homogeneous isotropic turbulence.
• Wavelet-based regularization shows distinct dynamical and statistical properties compared to other methods.

Conclusions:

• Wavelet-based denoising provides an effective adaptive regularization for Euler turbulence simulations.
• This method captures key features of 3D homogeneous isotropic turbulence.
• It offers a novel approach to turbulence modeling and comparison with existing regularization techniques.